Question #26044

The sun appears to move across the sky, because the earth spins on its axis. To a person standing on the earth, the sun subtends an angle of 9.28*0.001 rad. How much time (in seconds) does it take for the sun to move a distance equal to its own diameter?

Expert's answer

Travelling a distance equal to its own diameter equals travelling the angle of 9.28*0.001 rad.

the angular velocity ofsun is equal to the angular velocity of Earth:

w = 2*pi/T

T - period = twenty-fourhours

pi = 3.14 rad

angle = w*t

t - time

Thefore:

t = angle/w

In our case, angle= 9.28*0.001 rad

t = 9.28*0.001 / (2*pi/24*3600sec ) = 9.28*0.001*24*3600/2/3.14 sec = 127.7 sec

Answer: t = 127.7sec

the angular velocity ofsun is equal to the angular velocity of Earth:

w = 2*pi/T

T - period = twenty-fourhours

pi = 3.14 rad

angle = w*t

t - time

Thefore:

t = angle/w

In our case, angle= 9.28*0.001 rad

t = 9.28*0.001 / (2*pi/24*3600sec ) = 9.28*0.001*24*3600/2/3.14 sec = 127.7 sec

Answer: t = 127.7sec

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